Isomorphism and Subgraphs · Hard problem

Let $G$ be the $6$-cycle with vertices $1,\ldots,6$ and edges $12,23,34,45,56,16$. What is the smallest number $k$ such that removing some $k$ of $G$'s edges and adding $k$ new (non-)edges produces a graph isomorphic to two disjoint triangles ($K_3\cup K_3$)?